Problem 52844. Easy Sequences 42: Areas of Non-constructible Polygons

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Constructible_polygon\"><w:r><w:t>constructible polygon</w:t></w:r></w:hyperlink><w:r><w:t> is a regular polygon that can be constructed using only a compass and a straightedge.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Amazingly, Gauss found a way to identify which regular </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>-gon (abbreviation for a polygon, with </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> being the number of sides) is constructible, without even attempting to construct the polygon. </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Euler%27s_totient_function#Cyclotomy\"><w:r><w:t>Gauss's theorem states that an n-gon is contractible if and only if the totient of n is a power of 2.</w:t></w:r></w:hyperlink><w:r><w:t> (The </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Euler%27s_totient_function\"><w:r><w:t>Euler Totient Function</w:t></w:r></w:hyperlink><w:r><w:t> of a number </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> is defined as the number of integers from </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>1</w:t></w:r></w:customXml><w:r><w:t> to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> that are </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Coprime_integers\"><w:r><w:t>coprime</w:t></w:r></w:hyperlink><w:r><w:t> to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>.)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, the 3-gon (equilateral triangle) is constructible because the totient of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>3</w:t></w:r></w:customXml><w:r><w:t> is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2</w:t></w:r></w:customXml><w:r><w:t>. Similarly, the 5-gon (regular pentagon) is constructible because the totient of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>5</w:t></w:r></w:customXml><w:r><w:t> is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>4=2^2\n</w:t></w:r></w:customXml><w:r><w:t>. While, the 21-gon is non-constructible since the totient of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>21</w:t></w:r></w:customXml><w:r><w:t> is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>12</w:t></w:r></w:customXml><w:r><w:t>, not a power of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n=3\n</w:t></w:r></w:customXml><w:r><w:t> to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>20</w:t></w:r></w:customXml><w:r><w:t>, the number of sides of the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>-gons that are constructible are as follows </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20\\}</w:t></w:r></w:customXml><w:r><w:t> and their totients, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{2,2,4,2,4,4,4,8,8,16,8\\}</w:t></w:r></w:customXml><w:r><w:t>, are all powers of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2</w:t></w:r></w:customXml><w:r><w:t>. The non-constructible </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>-gons from </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>3</w:t></w:r></w:customXml><w:r><w:t> to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>20</w:t></w:r></w:customXml><w:r><w:t> are: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{7,9,11,13,14,18,19\\}</w:t></w:r></w:customXml><w:r><w:t>, and their totients are </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{6,6,10,12,6,6,18\\}</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given the limit of the number of sides </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>m</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, write a function that will output the sum of the areas of all </w:t></w:r><w:r><w:rPr><w:b/><w:u/></w:rPr><w:t>non-constructible</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> regular </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>-gons, for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>3 &lt; n \\le m</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, inscribed in a unit circle (</w:t></w:r><w:r><w:t>i.e.</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>radius = 1</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>).</w:t></w:r><w:r><w:t> </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"198\"/><w:attr w:name=\"width\" w:val=\"237\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>NOTES: </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Equality in float class is hard to establish. Therefore, for consistency, please </w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t>round-off each area</w:t></w:r><w:r><w:t> to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>4</w:t></w:r></w:customXml><w:r><w:t> decimal places, before taking the total.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>m=20</w:t></w:r></w:customXml><w:r><w:t>, the function should return </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>20.8231</w:t></w:r></w:customXml><w:r><w:t>, because the sum of areas of regular polygons with sides </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\{7,9,11,13,14,18,19\\}</w:t></w:r></w:customXml><w:r><w:t> = </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>2.7364+2.8925+2.9735+3.0207+3.0372+3.0782+3.0846=20.8231</w:t></w:r></w:customXml><w:r><w:t>. 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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 643.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 321.617px; transform-origin: 407px 321.617px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; ">A <a target='_blank' href = "https://en.wikipedia.org/wiki/Constructible_polygon">constructible polygon</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 274.5px 8px; transform-origin: 274.5px 8px; unicode-bidi: normal; "> is a regular polygon that can be constructed using only a compass and a straightedge.</div><div style="block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 174px 8px; transform-origin: 174px 8px; unicode-bidi: normal; ">Amazingly, Gauss found a way to identify which regular n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 119.5px 8px; transform-origin: 119.5px 8px; unicode-bidi: normal; ">-gon (abbreviation for a polygon, with n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67.5px 8px; transform-origin: 67.5px 8px; unicode-bidi: normal; "> being the number of sides) is constructible, without even attempting to construct the polygon. <a target='_blank' href = "https://en.wikipedia.org/wiki/Euler%27s_totient_function#Cyclotomy">Gauss's theorem states that an n-gon is contractible if and only if the totient of n is a power of 2.</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 19px 8px; transform-origin: 19px 8px; unicode-bidi: normal; "> (The <a target='_blank' href = "https://en.wikipedia.org/wiki/Euler%27s_totient_function">Euler Totient Function</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42px 8px; transform-origin: 42px 8px; unicode-bidi: normal; "> of a number n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; "> is defined as the number of integers from 1<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; "> to n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; "> that are <a target='_blank' href = "https://en.wikipedia.org/wiki/Coprime_integers">coprime</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; "> to n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; ">.)</div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 260.5px 8px; transform-origin: 260.5px 8px; unicode-bidi: normal; ">For example, the 3-gon (equilateral triangle) is constructible because the totient of 3<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; "> is 2<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93px 8px; transform-origin: 93px 8px; unicode-bidi: normal; ">. Similarly, the 5-gon (regular pentagon) is constructible because the totient of 5<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; "> is <img src="data:image/png;base64,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" style="width: 41.5px; height: 19px;" width="41.5" height="19"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 185.5px 8px; transform-origin: 185.5px 8px; unicode-bidi: normal; ">. While, the 21-gon is non-constructible since the totient of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABFUlEQVRYhe2W4Q2DIBBG3w5s4AIs0AmcwA26gRt0BWdgBHdwBWboCu2Pg4Q2ighimpQvuZgYuHuHx3nQ1NT0G7o50wU+OkCVQChgAl5f9gTuB0G8n+yEOhf4Gya0x46PtYSygWbAAkPwTq8E6Df298DonkspUI+cztbmMQhgEvyF67OADPEaUXzWU3WgCamhmOYrgVLkgeZfAbIuQMr1rw7UOeeW/U97CZAPkNocqwIppJBTaucSIIM0uiP/pGpAd6RujjqtAjRkwlQBKoE5HahPgNHEr/9pQBq5UbfIGoUUeXUgD7M4h1tm2W8BxUAeJjacpcxEICdng7VjDpBBsk4xw3pP6pCJcm3PxLERuKmpqem/9QYPHIoL20g4PAAAAABJRU5ErkJggg==" style="width: 18px; height: 18px;" width="18" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.45px 8px; transform-origin: 0.45px 8px; unicode-bidi: normal; "> is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABEElEQVRYhe2Waw2DMBRGj4c6qIEaQAEKcIADHMwCGioBD1hAwyywH22zbuPVB4Qs/ZIbEnJ7eyhfbwtFRUX3kgRE4JjKhsoN0gPzwcLCy/fjCbQpIEuF94Cknfgbxo9HDEwNdPY5BgANwAQ03jvF74fVMVBO3UGgGrM6azl+HX0FkGbbI4JPP50O1GM8tKXhSqAjckDDXYAmWydp++cCkrbGxP6vvQTI1UlanVxAAmPkJO/kBNKYBht6Fp4C1GJ8k+2ATQFqcsOkAJ0CEwtUH4BRRG7/UCCF2VHVRo7AmPx0IAcz2nFrMRHZAiTvdj/bYnswW5ez6DuRxNzshoXoWe62eiV/KTSZelJRUVHRX+sF+YKKC12KDjUAAAAASUVORK5CYII=" style="width: 18px; height: 18px;" width="18" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51px 8px; transform-origin: 51px 8px; unicode-bidi: normal; ">, not a power of 2<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; ">For <img src="data:image/png;base64,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" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; "> to <img src="data:image/png;base64,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" style="width: 18px; height: 18px;" width="18" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 88.5px 8px; transform-origin: 88.5px 8px; unicode-bidi: normal; ">, the number of sides of the n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.5px 8px; transform-origin: 133.5px 8px; unicode-bidi: normal; ">-gons that are constructible are as follows <img src="data:image/png;base64,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" style="width: 208px; height: 18.5px;" width="208" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "> and their totients, <img src="data:image/png;base64,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" style="width: 170.5px; height: 18.5px;" width="170.5" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; ">, are all powers of 2<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 75px 8px; transform-origin: 75px 8px; unicode-bidi: normal; ">. The non-constructible n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36px 8px; transform-origin: 36px 8px; unicode-bidi: normal; ">-gons from 3<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10px 8px; transform-origin: 10px 8px; unicode-bidi: normal; "> to <img src="data:image/png;base64,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" style="width: 18px; height: 18px;" width="18" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.5px 8px; transform-origin: 16.5px 8px; unicode-bidi: normal; "> are: <img src="data:image/png;base64,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" style="width: 145.5px; height: 18.5px;" width="145.5" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.5px 8px; transform-origin: 71.5px 8px; unicode-bidi: normal; ">, and their totients are <img src="data:image/png;base64,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" style="width: 130.5px; height: 18.5px;" width="130.5" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 134.5px 8px; transform-origin: 134.5px 8px; unicode-bidi: normal; ">Given the limit of the number of sides m<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 207.5px 8px; transform-origin: 207.5px 8px; unicode-bidi: normal; ">, write a function that will output the sum of the areas of all <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; ">non-constructible<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.5px 8px; transform-origin: 29.5px 8px; unicode-bidi: normal; "> regular n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36px 8px; transform-origin: 36px 8px; unicode-bidi: normal; ">-gons, for <img src="data:image/png;base64,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" style="width: 66px; height: 18px;" width="66" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 93px 8px; transform-origin: 93px 8px; unicode-bidi: normal; ">, inscribed in a unit circle (<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.5px 8px; transform-origin: 9.5px 8px; unicode-bidi: normal; ">i.e.<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 67px; height: 18px;" width="67" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; ">).<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "> </div><div style="block-size: 203.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 101.75px; text-align: left; transform-origin: 384px 101.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112px 8px; transform-origin: 112px 8px; unicode-bidi: normal; "> <img class="imageNode" style="vertical-align: baseline;width: 237px;height: 198px" 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" data-image-state="image-loaded" width="237" height="198"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.5px 8px; transform-origin: 27.5px 8px; unicode-bidi: normal; ">NOTES: </div><ul style="block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; "><li style="block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; ">Equality in float class is hard to establish. Therefore, for consistency, please round-off each area to 4 decimal places, before taking the total.</li><li style="block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; ">For <img src="data:image/png;base64,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" style="width: 47.5px; height: 18px;" width="47.5" height="18">, the function should return <img src="data:image/png;base64,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" style="width: 52px; height: 18px;" width="52" height="18">, because the sum of areas of regular polygons with sides <img src="data:image/png;base64,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" style="width: 145.5px; height: 18.5px;" width="145.5" height="18.5"> = <img src="data:image/png;base64,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" style="width: 460.5px; height: 18px;" width="460.5" height="18">. </li></ul></div></div>

A constructible polygon is a regular polygon that can be constructed using only a compass and a straightedge.
Amazingly, Gauss found a way to identify which regular -gon (abbreviation for a polygon, with  being the number of sides) is constructible, without even attempting to construct the polygon. Gauss's theorem states that an n-gon is contractible if and only if the totient of n is a power of 2. (The Euler Totient Function of a number  is defined as the number of integers from  to  that are coprime to .)
For example, the 3-gon (equilateral triangle) is constructible because the totient of  is . Similarly, the 5-gon (regular pentagon) is constructible because the totient of  is . While, the 21-gon is non-constructible since the totient of  is , not a power of .
For  to , the number of sides of the -gons that are constructible are as follows  and their totients, , are all powers of . The non-constructible -gons from  to  are: , and their totients are .
Given the limit of the number of sides , write a function that will output the sum of the areas of all non-constructible regular -gons, for , inscribed in a unit circle (i.e. ). 
                                                        
NOTES: 
Equality in float class is hard to establish. Therefore, for consistency, please round-off each area to  decimal places, before taking the total.
For , the function should return , because the sum of areas of regular polygons with sides  = .

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Problem 52844. Easy Sequences 42: Areas of Non-constructible Polygons

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